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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.analysis.differentiation;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.io.Serializable;<a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.analysis.UnivariateMatrixFunction;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.analysis.UnivariateVectorFunction;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.NotPositiveException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.NumberIsTooLargeException;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.28"></a>
<FONT color="green">029</FONT>    <a name="line.29"></a>
<FONT color="green">030</FONT>    /** Univariate functions differentiator using finite differences.<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * This class creates some wrapper objects around regular<a name="line.32"></a>
<FONT color="green">033</FONT>     * {@link UnivariateFunction univariate functions} (or {@link<a name="line.33"></a>
<FONT color="green">034</FONT>     * UnivariateVectorFunction univariate vector functions} or {@link<a name="line.34"></a>
<FONT color="green">035</FONT>     * UnivariateMatrixFunction univariate matrix functions}). These<a name="line.35"></a>
<FONT color="green">036</FONT>     * wrapper objects compute derivatives in addition to function<a name="line.36"></a>
<FONT color="green">037</FONT>     * value.<a name="line.37"></a>
<FONT color="green">038</FONT>     * &lt;/p&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     * &lt;p&gt;<a name="line.39"></a>
<FONT color="green">040</FONT>     * The wrapper objects work by calling the underlying function on<a name="line.40"></a>
<FONT color="green">041</FONT>     * a sampling grid around the current point and performing polynomial<a name="line.41"></a>
<FONT color="green">042</FONT>     * interpolation. A finite differences scheme with n points is<a name="line.42"></a>
<FONT color="green">043</FONT>     * theoretically able to compute derivatives up to order n-1, but<a name="line.43"></a>
<FONT color="green">044</FONT>     * it is generally better to have a slight margin. The step size must<a name="line.44"></a>
<FONT color="green">045</FONT>     * also be small enough in order for the polynomial approximation to<a name="line.45"></a>
<FONT color="green">046</FONT>     * be good in the current point neighborhood, but it should not be too<a name="line.46"></a>
<FONT color="green">047</FONT>     * small because numerical instability appears quickly (there are several<a name="line.47"></a>
<FONT color="green">048</FONT>     * differences of close points). Choosing the number of points and<a name="line.48"></a>
<FONT color="green">049</FONT>     * the step size is highly problem dependent.<a name="line.49"></a>
<FONT color="green">050</FONT>     * &lt;/p&gt;<a name="line.50"></a>
<FONT color="green">051</FONT>     * &lt;p&gt;<a name="line.51"></a>
<FONT color="green">052</FONT>     * As an example of good and bad settings, lets consider the quintic<a name="line.52"></a>
<FONT color="green">053</FONT>     * polynomial function {@code f(x) = (x-1)*(x-0.5)*x*(x+0.5)*(x+1)}.<a name="line.53"></a>
<FONT color="green">054</FONT>     * Since it is a polynomial, finite differences with at least 6 points<a name="line.54"></a>
<FONT color="green">055</FONT>     * should theoretically recover the exact same polynomial and hence<a name="line.55"></a>
<FONT color="green">056</FONT>     * compute accurate derivatives for any order. However, due to numerical<a name="line.56"></a>
<FONT color="green">057</FONT>     * errors, we get the following results for a 7 points finite differences<a name="line.57"></a>
<FONT color="green">058</FONT>     * for abscissae in the [-10, 10] range:<a name="line.58"></a>
<FONT color="green">059</FONT>     * &lt;ul&gt;<a name="line.59"></a>
<FONT color="green">060</FONT>     *   &lt;li&gt;step size = 0.25, second order derivative error about 9.97e-10&lt;/li&gt;<a name="line.60"></a>
<FONT color="green">061</FONT>     *   &lt;li&gt;step size = 0.25, fourth order derivative error about 5.43e-8&lt;/li&gt;<a name="line.61"></a>
<FONT color="green">062</FONT>     *   &lt;li&gt;step size = 1.0e-6, second order derivative error about 148&lt;/li&gt;<a name="line.62"></a>
<FONT color="green">063</FONT>     *   &lt;li&gt;step size = 1.0e-6, fourth order derivative error about 6.35e+14&lt;/li&gt;<a name="line.63"></a>
<FONT color="green">064</FONT>     * &lt;/ul&gt;<a name="line.64"></a>
<FONT color="green">065</FONT>     * This example shows that the small step size is really bad, even simply<a name="line.65"></a>
<FONT color="green">066</FONT>     * for second order derivative!<a name="line.66"></a>
<FONT color="green">067</FONT>     * &lt;/p&gt;<a name="line.67"></a>
<FONT color="green">068</FONT>     * @version $Id: FiniteDifferencesDifferentiator.java 1420666 2012-12-12 13:33:20Z erans $<a name="line.68"></a>
<FONT color="green">069</FONT>     * @since 3.1<a name="line.69"></a>
<FONT color="green">070</FONT>     */<a name="line.70"></a>
<FONT color="green">071</FONT>    public class FiniteDifferencesDifferentiator<a name="line.71"></a>
<FONT color="green">072</FONT>        implements UnivariateFunctionDifferentiator, UnivariateVectorFunctionDifferentiator,<a name="line.72"></a>
<FONT color="green">073</FONT>                   UnivariateMatrixFunctionDifferentiator, Serializable {<a name="line.73"></a>
<FONT color="green">074</FONT>    <a name="line.74"></a>
<FONT color="green">075</FONT>        /** Serializable UID. */<a name="line.75"></a>
<FONT color="green">076</FONT>        private static final long serialVersionUID = 20120917L;<a name="line.76"></a>
<FONT color="green">077</FONT>    <a name="line.77"></a>
<FONT color="green">078</FONT>        /** Number of points to use. */<a name="line.78"></a>
<FONT color="green">079</FONT>        private final int nbPoints;<a name="line.79"></a>
<FONT color="green">080</FONT>    <a name="line.80"></a>
<FONT color="green">081</FONT>        /** Step size. */<a name="line.81"></a>
<FONT color="green">082</FONT>        private final double stepSize;<a name="line.82"></a>
<FONT color="green">083</FONT>    <a name="line.83"></a>
<FONT color="green">084</FONT>        /** Half sample span. */<a name="line.84"></a>
<FONT color="green">085</FONT>        private final double halfSampleSpan;<a name="line.85"></a>
<FONT color="green">086</FONT>    <a name="line.86"></a>
<FONT color="green">087</FONT>        /** Lower bound for independent variable. */<a name="line.87"></a>
<FONT color="green">088</FONT>        private final double tMin;<a name="line.88"></a>
<FONT color="green">089</FONT>    <a name="line.89"></a>
<FONT color="green">090</FONT>        /** Upper bound for independent variable. */<a name="line.90"></a>
<FONT color="green">091</FONT>        private final double tMax;<a name="line.91"></a>
<FONT color="green">092</FONT>    <a name="line.92"></a>
<FONT color="green">093</FONT>        /**<a name="line.93"></a>
<FONT color="green">094</FONT>         * Build a differentiator with number of points and step size when independent variable is unbounded.<a name="line.94"></a>
<FONT color="green">095</FONT>         * &lt;p&gt;<a name="line.95"></a>
<FONT color="green">096</FONT>         * Beware that wrong settings for the finite differences differentiator<a name="line.96"></a>
<FONT color="green">097</FONT>         * can lead to highly unstable and inaccurate results, especially for<a name="line.97"></a>
<FONT color="green">098</FONT>         * high derivation orders. Using very small step sizes is often a<a name="line.98"></a>
<FONT color="green">099</FONT>         * &lt;em&gt;bad&lt;/em&gt; idea.<a name="line.99"></a>
<FONT color="green">100</FONT>         * &lt;/p&gt;<a name="line.100"></a>
<FONT color="green">101</FONT>         * @param nbPoints number of points to use<a name="line.101"></a>
<FONT color="green">102</FONT>         * @param stepSize step size (gap between each point)<a name="line.102"></a>
<FONT color="green">103</FONT>         * @exception NotPositiveException if {@code stepsize &lt;= 0} (note that<a name="line.103"></a>
<FONT color="green">104</FONT>         * {@link NotPositiveException} extends {@link NumberIsTooSmallException})<a name="line.104"></a>
<FONT color="green">105</FONT>         * @exception NumberIsTooSmallException {@code nbPoint &lt;= 1}<a name="line.105"></a>
<FONT color="green">106</FONT>         */<a name="line.106"></a>
<FONT color="green">107</FONT>        public FiniteDifferencesDifferentiator(final int nbPoints, final double stepSize)<a name="line.107"></a>
<FONT color="green">108</FONT>            throws NotPositiveException, NumberIsTooSmallException {<a name="line.108"></a>
<FONT color="green">109</FONT>            this(nbPoints, stepSize, Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);<a name="line.109"></a>
<FONT color="green">110</FONT>        }<a name="line.110"></a>
<FONT color="green">111</FONT>    <a name="line.111"></a>
<FONT color="green">112</FONT>        /**<a name="line.112"></a>
<FONT color="green">113</FONT>         * Build a differentiator with number of points and step size when independent variable is bounded.<a name="line.113"></a>
<FONT color="green">114</FONT>         * &lt;p&gt;<a name="line.114"></a>
<FONT color="green">115</FONT>         * When the independent variable is bounded (tLower &amp;lt; t &amp;lt; tUpper), the sampling<a name="line.115"></a>
<FONT color="green">116</FONT>         * points used for differentiation will be adapted to ensure the constraint holds<a name="line.116"></a>
<FONT color="green">117</FONT>         * even near the boundaries. This means the sample will not be centered anymore in<a name="line.117"></a>
<FONT color="green">118</FONT>         * these cases. At an extreme case, computing derivatives exactly at the lower bound<a name="line.118"></a>
<FONT color="green">119</FONT>         * will lead the sample to be entirely on the right side of the derivation point.<a name="line.119"></a>
<FONT color="green">120</FONT>         * &lt;/p&gt;<a name="line.120"></a>
<FONT color="green">121</FONT>         * &lt;p&gt;<a name="line.121"></a>
<FONT color="green">122</FONT>         * Note that the boundaries are considered to be excluded for function evaluation.<a name="line.122"></a>
<FONT color="green">123</FONT>         * &lt;/p&gt;<a name="line.123"></a>
<FONT color="green">124</FONT>         * &lt;p&gt;<a name="line.124"></a>
<FONT color="green">125</FONT>         * Beware that wrong settings for the finite differences differentiator<a name="line.125"></a>
<FONT color="green">126</FONT>         * can lead to highly unstable and inaccurate results, especially for<a name="line.126"></a>
<FONT color="green">127</FONT>         * high derivation orders. Using very small step sizes is often a<a name="line.127"></a>
<FONT color="green">128</FONT>         * &lt;em&gt;bad&lt;/em&gt; idea.<a name="line.128"></a>
<FONT color="green">129</FONT>         * &lt;/p&gt;<a name="line.129"></a>
<FONT color="green">130</FONT>         * @param nbPoints number of points to use<a name="line.130"></a>
<FONT color="green">131</FONT>         * @param stepSize step size (gap between each point)<a name="line.131"></a>
<FONT color="green">132</FONT>         * @param tLower lower bound for independent variable (may be {@code Double.NEGATIVE_INFINITY}<a name="line.132"></a>
<FONT color="green">133</FONT>         * if there are no lower bounds)<a name="line.133"></a>
<FONT color="green">134</FONT>         * @param tUpper upper bound for independent variable (may be {@code Double.POSITIVE_INFINITY}<a name="line.134"></a>
<FONT color="green">135</FONT>         * if there are no upper bounds)<a name="line.135"></a>
<FONT color="green">136</FONT>         * @exception NotPositiveException if {@code stepsize &lt;= 0} (note that<a name="line.136"></a>
<FONT color="green">137</FONT>         * {@link NotPositiveException} extends {@link NumberIsTooSmallException})<a name="line.137"></a>
<FONT color="green">138</FONT>         * @exception NumberIsTooSmallException {@code nbPoint &lt;= 1}<a name="line.138"></a>
<FONT color="green">139</FONT>         * @exception NumberIsTooLargeException {@code stepSize * (nbPoints - 1) &gt;= tUpper - tLower}<a name="line.139"></a>
<FONT color="green">140</FONT>         */<a name="line.140"></a>
<FONT color="green">141</FONT>        public FiniteDifferencesDifferentiator(final int nbPoints, final double stepSize,<a name="line.141"></a>
<FONT color="green">142</FONT>                                               final double tLower, final double tUpper)<a name="line.142"></a>
<FONT color="green">143</FONT>                throws NotPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {<a name="line.143"></a>
<FONT color="green">144</FONT>    <a name="line.144"></a>
<FONT color="green">145</FONT>            if (nbPoints &lt;= 1) {<a name="line.145"></a>
<FONT color="green">146</FONT>                throw new NumberIsTooSmallException(stepSize, 1, false);<a name="line.146"></a>
<FONT color="green">147</FONT>            }<a name="line.147"></a>
<FONT color="green">148</FONT>            this.nbPoints = nbPoints;<a name="line.148"></a>
<FONT color="green">149</FONT>    <a name="line.149"></a>
<FONT color="green">150</FONT>            if (stepSize &lt;= 0) {<a name="line.150"></a>
<FONT color="green">151</FONT>                throw new NotPositiveException(stepSize);<a name="line.151"></a>
<FONT color="green">152</FONT>            }<a name="line.152"></a>
<FONT color="green">153</FONT>            this.stepSize = stepSize;<a name="line.153"></a>
<FONT color="green">154</FONT>    <a name="line.154"></a>
<FONT color="green">155</FONT>            halfSampleSpan = 0.5 * stepSize * (nbPoints - 1);<a name="line.155"></a>
<FONT color="green">156</FONT>            if (2 * halfSampleSpan &gt;= tUpper - tLower) {<a name="line.156"></a>
<FONT color="green">157</FONT>                throw new NumberIsTooLargeException(2 * halfSampleSpan, tUpper - tLower, false);<a name="line.157"></a>
<FONT color="green">158</FONT>            }<a name="line.158"></a>
<FONT color="green">159</FONT>            final double safety = FastMath.ulp(halfSampleSpan);<a name="line.159"></a>
<FONT color="green">160</FONT>            this.tMin = tLower + halfSampleSpan + safety;<a name="line.160"></a>
<FONT color="green">161</FONT>            this.tMax = tUpper - halfSampleSpan - safety;<a name="line.161"></a>
<FONT color="green">162</FONT>    <a name="line.162"></a>
<FONT color="green">163</FONT>        }<a name="line.163"></a>
<FONT color="green">164</FONT>    <a name="line.164"></a>
<FONT color="green">165</FONT>        /**<a name="line.165"></a>
<FONT color="green">166</FONT>         * Get the number of points to use.<a name="line.166"></a>
<FONT color="green">167</FONT>         * @return number of points to use<a name="line.167"></a>
<FONT color="green">168</FONT>         */<a name="line.168"></a>
<FONT color="green">169</FONT>        public int getNbPoints() {<a name="line.169"></a>
<FONT color="green">170</FONT>            return nbPoints;<a name="line.170"></a>
<FONT color="green">171</FONT>        }<a name="line.171"></a>
<FONT color="green">172</FONT>    <a name="line.172"></a>
<FONT color="green">173</FONT>        /**<a name="line.173"></a>
<FONT color="green">174</FONT>         * Get the step size.<a name="line.174"></a>
<FONT color="green">175</FONT>         * @return step size<a name="line.175"></a>
<FONT color="green">176</FONT>         */<a name="line.176"></a>
<FONT color="green">177</FONT>        public double getStepSize() {<a name="line.177"></a>
<FONT color="green">178</FONT>            return stepSize;<a name="line.178"></a>
<FONT color="green">179</FONT>        }<a name="line.179"></a>
<FONT color="green">180</FONT>    <a name="line.180"></a>
<FONT color="green">181</FONT>        /**<a name="line.181"></a>
<FONT color="green">182</FONT>         * Evaluate derivatives from a sample.<a name="line.182"></a>
<FONT color="green">183</FONT>         * &lt;p&gt;<a name="line.183"></a>
<FONT color="green">184</FONT>         * Evaluation is done using divided differences.<a name="line.184"></a>
<FONT color="green">185</FONT>         * &lt;/p&gt;<a name="line.185"></a>
<FONT color="green">186</FONT>         * @param t evaluation abscissa value and derivatives<a name="line.186"></a>
<FONT color="green">187</FONT>         * @param t0 first sample point abscissa<a name="line.187"></a>
<FONT color="green">188</FONT>         * @param y function values sample {@code y[i] = f(t[i]) = f(t0 + i * stepSize)}<a name="line.188"></a>
<FONT color="green">189</FONT>         * @return value and derivatives at {@code t}<a name="line.189"></a>
<FONT color="green">190</FONT>         * @exception NumberIsTooLargeException if the requested derivation order<a name="line.190"></a>
<FONT color="green">191</FONT>         * is larger or equal to the number of points<a name="line.191"></a>
<FONT color="green">192</FONT>         */<a name="line.192"></a>
<FONT color="green">193</FONT>        private DerivativeStructure evaluate(final DerivativeStructure t, final double t0,<a name="line.193"></a>
<FONT color="green">194</FONT>                                             final double[] y)<a name="line.194"></a>
<FONT color="green">195</FONT>            throws NumberIsTooLargeException {<a name="line.195"></a>
<FONT color="green">196</FONT>    <a name="line.196"></a>
<FONT color="green">197</FONT>            // create divided differences diagonal arrays<a name="line.197"></a>
<FONT color="green">198</FONT>            final double[] top    = new double[nbPoints];<a name="line.198"></a>
<FONT color="green">199</FONT>            final double[] bottom = new double[nbPoints];<a name="line.199"></a>
<FONT color="green">200</FONT>    <a name="line.200"></a>
<FONT color="green">201</FONT>            for (int i = 0; i &lt; nbPoints; ++i) {<a name="line.201"></a>
<FONT color="green">202</FONT>    <a name="line.202"></a>
<FONT color="green">203</FONT>                // update the bottom diagonal of the divided differences array<a name="line.203"></a>
<FONT color="green">204</FONT>                bottom[i] = y[i];<a name="line.204"></a>
<FONT color="green">205</FONT>                for (int j = 1; j &lt;= i; ++j) {<a name="line.205"></a>
<FONT color="green">206</FONT>                    bottom[i - j] = (bottom[i - j + 1] - bottom[i - j]) / (j * stepSize);<a name="line.206"></a>
<FONT color="green">207</FONT>                }<a name="line.207"></a>
<FONT color="green">208</FONT>    <a name="line.208"></a>
<FONT color="green">209</FONT>                // update the top diagonal of the divided differences array<a name="line.209"></a>
<FONT color="green">210</FONT>                top[i] = bottom[0];<a name="line.210"></a>
<FONT color="green">211</FONT>    <a name="line.211"></a>
<FONT color="green">212</FONT>            }<a name="line.212"></a>
<FONT color="green">213</FONT>    <a name="line.213"></a>
<FONT color="green">214</FONT>            // evaluate interpolation polynomial (represented by top diagonal) at t<a name="line.214"></a>
<FONT color="green">215</FONT>            final int order            = t.getOrder();<a name="line.215"></a>
<FONT color="green">216</FONT>            final int parameters       = t.getFreeParameters();<a name="line.216"></a>
<FONT color="green">217</FONT>            final double[] derivatives = t.getAllDerivatives();<a name="line.217"></a>
<FONT color="green">218</FONT>            final double dt0           = t.getValue() - t0;<a name="line.218"></a>
<FONT color="green">219</FONT>            DerivativeStructure interpolation = new DerivativeStructure(parameters, order, 0.0);<a name="line.219"></a>
<FONT color="green">220</FONT>            DerivativeStructure monomial = null;<a name="line.220"></a>
<FONT color="green">221</FONT>            for (int i = 0; i &lt; nbPoints; ++i) {<a name="line.221"></a>
<FONT color="green">222</FONT>                if (i == 0) {<a name="line.222"></a>
<FONT color="green">223</FONT>                    // start with monomial(t) = 1<a name="line.223"></a>
<FONT color="green">224</FONT>                    monomial = new DerivativeStructure(parameters, order, 1.0);<a name="line.224"></a>
<FONT color="green">225</FONT>                } else {<a name="line.225"></a>
<FONT color="green">226</FONT>                    // monomial(t) = (t - t0) * (t - t1) * ... * (t - t(i-1))<a name="line.226"></a>
<FONT color="green">227</FONT>                    derivatives[0] = dt0 - (i - 1) * stepSize;<a name="line.227"></a>
<FONT color="green">228</FONT>                    final DerivativeStructure deltaX = new DerivativeStructure(parameters, order, derivatives);<a name="line.228"></a>
<FONT color="green">229</FONT>                    monomial = monomial.multiply(deltaX);<a name="line.229"></a>
<FONT color="green">230</FONT>                }<a name="line.230"></a>
<FONT color="green">231</FONT>                interpolation = interpolation.add(monomial.multiply(top[i]));<a name="line.231"></a>
<FONT color="green">232</FONT>            }<a name="line.232"></a>
<FONT color="green">233</FONT>    <a name="line.233"></a>
<FONT color="green">234</FONT>            return interpolation;<a name="line.234"></a>
<FONT color="green">235</FONT>    <a name="line.235"></a>
<FONT color="green">236</FONT>        }<a name="line.236"></a>
<FONT color="green">237</FONT>    <a name="line.237"></a>
<FONT color="green">238</FONT>        /** {@inheritDoc}<a name="line.238"></a>
<FONT color="green">239</FONT>         * &lt;p&gt;The returned object cannot compute derivatives to arbitrary orders. The<a name="line.239"></a>
<FONT color="green">240</FONT>         * value function will throw a {@link NumberIsTooLargeException} if the requested<a name="line.240"></a>
<FONT color="green">241</FONT>         * derivation order is larger or equal to the number of points.<a name="line.241"></a>
<FONT color="green">242</FONT>         * &lt;/p&gt;<a name="line.242"></a>
<FONT color="green">243</FONT>         */<a name="line.243"></a>
<FONT color="green">244</FONT>        public UnivariateDifferentiableFunction differentiate(final UnivariateFunction function) {<a name="line.244"></a>
<FONT color="green">245</FONT>            return new UnivariateDifferentiableFunction() {<a name="line.245"></a>
<FONT color="green">246</FONT>    <a name="line.246"></a>
<FONT color="green">247</FONT>                /** {@inheritDoc} */<a name="line.247"></a>
<FONT color="green">248</FONT>                public double value(final double x) throws MathIllegalArgumentException {<a name="line.248"></a>
<FONT color="green">249</FONT>                    return function.value(x);<a name="line.249"></a>
<FONT color="green">250</FONT>                }<a name="line.250"></a>
<FONT color="green">251</FONT>    <a name="line.251"></a>
<FONT color="green">252</FONT>                /** {@inheritDoc} */<a name="line.252"></a>
<FONT color="green">253</FONT>                public DerivativeStructure value(final DerivativeStructure t)<a name="line.253"></a>
<FONT color="green">254</FONT>                    throws MathIllegalArgumentException {<a name="line.254"></a>
<FONT color="green">255</FONT>    <a name="line.255"></a>
<FONT color="green">256</FONT>                    // check we can achieve the requested derivation order with the sample<a name="line.256"></a>
<FONT color="green">257</FONT>                    if (t.getOrder() &gt;= nbPoints) {<a name="line.257"></a>
<FONT color="green">258</FONT>                        throw new NumberIsTooLargeException(t.getOrder(), nbPoints, false);<a name="line.258"></a>
<FONT color="green">259</FONT>                    }<a name="line.259"></a>
<FONT color="green">260</FONT>    <a name="line.260"></a>
<FONT color="green">261</FONT>                    // compute sample position, trying to be centered if possible<a name="line.261"></a>
<FONT color="green">262</FONT>                    final double t0 = FastMath.max(FastMath.min(t.getValue(), tMax), tMin) - halfSampleSpan;<a name="line.262"></a>
<FONT color="green">263</FONT>    <a name="line.263"></a>
<FONT color="green">264</FONT>                    // compute sample points<a name="line.264"></a>
<FONT color="green">265</FONT>                    final double[] y = new double[nbPoints];<a name="line.265"></a>
<FONT color="green">266</FONT>                    for (int i = 0; i &lt; nbPoints; ++i) {<a name="line.266"></a>
<FONT color="green">267</FONT>                        y[i] = function.value(t0 + i * stepSize);<a name="line.267"></a>
<FONT color="green">268</FONT>                    }<a name="line.268"></a>
<FONT color="green">269</FONT>    <a name="line.269"></a>
<FONT color="green">270</FONT>                    // evaluate derivatives<a name="line.270"></a>
<FONT color="green">271</FONT>                    return evaluate(t, t0, y);<a name="line.271"></a>
<FONT color="green">272</FONT>    <a name="line.272"></a>
<FONT color="green">273</FONT>                }<a name="line.273"></a>
<FONT color="green">274</FONT>    <a name="line.274"></a>
<FONT color="green">275</FONT>            };<a name="line.275"></a>
<FONT color="green">276</FONT>        }<a name="line.276"></a>
<FONT color="green">277</FONT>    <a name="line.277"></a>
<FONT color="green">278</FONT>        /** {@inheritDoc}<a name="line.278"></a>
<FONT color="green">279</FONT>         * &lt;p&gt;The returned object cannot compute derivatives to arbitrary orders. The<a name="line.279"></a>
<FONT color="green">280</FONT>         * value function will throw a {@link NumberIsTooLargeException} if the requested<a name="line.280"></a>
<FONT color="green">281</FONT>         * derivation order is larger or equal to the number of points.<a name="line.281"></a>
<FONT color="green">282</FONT>         * &lt;/p&gt;<a name="line.282"></a>
<FONT color="green">283</FONT>         */<a name="line.283"></a>
<FONT color="green">284</FONT>        public UnivariateDifferentiableVectorFunction differentiate(final UnivariateVectorFunction function) {<a name="line.284"></a>
<FONT color="green">285</FONT>            return new UnivariateDifferentiableVectorFunction() {<a name="line.285"></a>
<FONT color="green">286</FONT>    <a name="line.286"></a>
<FONT color="green">287</FONT>                /** {@inheritDoc} */<a name="line.287"></a>
<FONT color="green">288</FONT>                public double[]value(final double x) throws MathIllegalArgumentException {<a name="line.288"></a>
<FONT color="green">289</FONT>                    return function.value(x);<a name="line.289"></a>
<FONT color="green">290</FONT>                }<a name="line.290"></a>
<FONT color="green">291</FONT>    <a name="line.291"></a>
<FONT color="green">292</FONT>                /** {@inheritDoc} */<a name="line.292"></a>
<FONT color="green">293</FONT>                public DerivativeStructure[] value(final DerivativeStructure t)<a name="line.293"></a>
<FONT color="green">294</FONT>                    throws MathIllegalArgumentException {<a name="line.294"></a>
<FONT color="green">295</FONT>    <a name="line.295"></a>
<FONT color="green">296</FONT>                    // check we can achieve the requested derivation order with the sample<a name="line.296"></a>
<FONT color="green">297</FONT>                    if (t.getOrder() &gt;= nbPoints) {<a name="line.297"></a>
<FONT color="green">298</FONT>                        throw new NumberIsTooLargeException(t.getOrder(), nbPoints, false);<a name="line.298"></a>
<FONT color="green">299</FONT>                    }<a name="line.299"></a>
<FONT color="green">300</FONT>    <a name="line.300"></a>
<FONT color="green">301</FONT>                    // compute sample position, trying to be centered if possible<a name="line.301"></a>
<FONT color="green">302</FONT>                    final double t0 = FastMath.max(FastMath.min(t.getValue(), tMax), tMin) - halfSampleSpan;<a name="line.302"></a>
<FONT color="green">303</FONT>    <a name="line.303"></a>
<FONT color="green">304</FONT>                    // compute sample points<a name="line.304"></a>
<FONT color="green">305</FONT>                    double[][] y = null;<a name="line.305"></a>
<FONT color="green">306</FONT>                    for (int i = 0; i &lt; nbPoints; ++i) {<a name="line.306"></a>
<FONT color="green">307</FONT>                        final double[] v = function.value(t0 + i * stepSize);<a name="line.307"></a>
<FONT color="green">308</FONT>                        if (i == 0) {<a name="line.308"></a>
<FONT color="green">309</FONT>                            y = new double[v.length][nbPoints];<a name="line.309"></a>
<FONT color="green">310</FONT>                        }<a name="line.310"></a>
<FONT color="green">311</FONT>                        for (int j = 0; j &lt; v.length; ++j) {<a name="line.311"></a>
<FONT color="green">312</FONT>                            y[j][i] = v[j];<a name="line.312"></a>
<FONT color="green">313</FONT>                        }<a name="line.313"></a>
<FONT color="green">314</FONT>                    }<a name="line.314"></a>
<FONT color="green">315</FONT>    <a name="line.315"></a>
<FONT color="green">316</FONT>                    // evaluate derivatives<a name="line.316"></a>
<FONT color="green">317</FONT>                    final DerivativeStructure[] value = new DerivativeStructure[y.length];<a name="line.317"></a>
<FONT color="green">318</FONT>                    for (int j = 0; j &lt; value.length; ++j) {<a name="line.318"></a>
<FONT color="green">319</FONT>                        value[j] = evaluate(t, t0, y[j]);<a name="line.319"></a>
<FONT color="green">320</FONT>                    }<a name="line.320"></a>
<FONT color="green">321</FONT>    <a name="line.321"></a>
<FONT color="green">322</FONT>                    return value;<a name="line.322"></a>
<FONT color="green">323</FONT>    <a name="line.323"></a>
<FONT color="green">324</FONT>                }<a name="line.324"></a>
<FONT color="green">325</FONT>    <a name="line.325"></a>
<FONT color="green">326</FONT>            };<a name="line.326"></a>
<FONT color="green">327</FONT>        }<a name="line.327"></a>
<FONT color="green">328</FONT>    <a name="line.328"></a>
<FONT color="green">329</FONT>        /** {@inheritDoc}<a name="line.329"></a>
<FONT color="green">330</FONT>         * &lt;p&gt;The returned object cannot compute derivatives to arbitrary orders. The<a name="line.330"></a>
<FONT color="green">331</FONT>         * value function will throw a {@link NumberIsTooLargeException} if the requested<a name="line.331"></a>
<FONT color="green">332</FONT>         * derivation order is larger or equal to the number of points.<a name="line.332"></a>
<FONT color="green">333</FONT>         * &lt;/p&gt;<a name="line.333"></a>
<FONT color="green">334</FONT>         */<a name="line.334"></a>
<FONT color="green">335</FONT>        public UnivariateDifferentiableMatrixFunction differentiate(final UnivariateMatrixFunction function) {<a name="line.335"></a>
<FONT color="green">336</FONT>            return new UnivariateDifferentiableMatrixFunction() {<a name="line.336"></a>
<FONT color="green">337</FONT>    <a name="line.337"></a>
<FONT color="green">338</FONT>                /** {@inheritDoc} */<a name="line.338"></a>
<FONT color="green">339</FONT>                public double[][]  value(final double x) throws MathIllegalArgumentException {<a name="line.339"></a>
<FONT color="green">340</FONT>                    return function.value(x);<a name="line.340"></a>
<FONT color="green">341</FONT>                }<a name="line.341"></a>
<FONT color="green">342</FONT>    <a name="line.342"></a>
<FONT color="green">343</FONT>                /** {@inheritDoc} */<a name="line.343"></a>
<FONT color="green">344</FONT>                public DerivativeStructure[][]  value(final DerivativeStructure t)<a name="line.344"></a>
<FONT color="green">345</FONT>                    throws MathIllegalArgumentException {<a name="line.345"></a>
<FONT color="green">346</FONT>    <a name="line.346"></a>
<FONT color="green">347</FONT>                    // check we can achieve the requested derivation order with the sample<a name="line.347"></a>
<FONT color="green">348</FONT>                    if (t.getOrder() &gt;= nbPoints) {<a name="line.348"></a>
<FONT color="green">349</FONT>                        throw new NumberIsTooLargeException(t.getOrder(), nbPoints, false);<a name="line.349"></a>
<FONT color="green">350</FONT>                    }<a name="line.350"></a>
<FONT color="green">351</FONT>    <a name="line.351"></a>
<FONT color="green">352</FONT>                    // compute sample position, trying to be centered if possible<a name="line.352"></a>
<FONT color="green">353</FONT>                    final double t0 = FastMath.max(FastMath.min(t.getValue(), tMax), tMin) - halfSampleSpan;<a name="line.353"></a>
<FONT color="green">354</FONT>    <a name="line.354"></a>
<FONT color="green">355</FONT>                    // compute sample points<a name="line.355"></a>
<FONT color="green">356</FONT>                    double[][][] y = null;<a name="line.356"></a>
<FONT color="green">357</FONT>                    for (int i = 0; i &lt; nbPoints; ++i) {<a name="line.357"></a>
<FONT color="green">358</FONT>                        final double[][] v = function.value(t0 + i * stepSize);<a name="line.358"></a>
<FONT color="green">359</FONT>                        if (i == 0) {<a name="line.359"></a>
<FONT color="green">360</FONT>                            y = new double[v.length][v[0].length][nbPoints];<a name="line.360"></a>
<FONT color="green">361</FONT>                        }<a name="line.361"></a>
<FONT color="green">362</FONT>                        for (int j = 0; j &lt; v.length; ++j) {<a name="line.362"></a>
<FONT color="green">363</FONT>                            for (int k = 0; k &lt; v[j].length; ++k) {<a name="line.363"></a>
<FONT color="green">364</FONT>                                y[j][k][i] = v[j][k];<a name="line.364"></a>
<FONT color="green">365</FONT>                            }<a name="line.365"></a>
<FONT color="green">366</FONT>                        }<a name="line.366"></a>
<FONT color="green">367</FONT>                    }<a name="line.367"></a>
<FONT color="green">368</FONT>    <a name="line.368"></a>
<FONT color="green">369</FONT>                    // evaluate derivatives<a name="line.369"></a>
<FONT color="green">370</FONT>                    final DerivativeStructure[][] value = new DerivativeStructure[y.length][y[0].length];<a name="line.370"></a>
<FONT color="green">371</FONT>                    for (int j = 0; j &lt; value.length; ++j) {<a name="line.371"></a>
<FONT color="green">372</FONT>                        for (int k = 0; k &lt; y[j].length; ++k) {<a name="line.372"></a>
<FONT color="green">373</FONT>                            value[j][k] = evaluate(t, t0, y[j][k]);<a name="line.373"></a>
<FONT color="green">374</FONT>                        }<a name="line.374"></a>
<FONT color="green">375</FONT>                    }<a name="line.375"></a>
<FONT color="green">376</FONT>    <a name="line.376"></a>
<FONT color="green">377</FONT>                    return value;<a name="line.377"></a>
<FONT color="green">378</FONT>    <a name="line.378"></a>
<FONT color="green">379</FONT>                }<a name="line.379"></a>
<FONT color="green">380</FONT>    <a name="line.380"></a>
<FONT color="green">381</FONT>            };<a name="line.381"></a>
<FONT color="green">382</FONT>        }<a name="line.382"></a>
<FONT color="green">383</FONT>    <a name="line.383"></a>
<FONT color="green">384</FONT>    }<a name="line.384"></a>




























































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